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Theoretical and Applicational Aspects of Fuzzy Implication Functions

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Quantitative Logic and Soft Computing 2016

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 510))

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Abstract

Fuzzy implication functions are one of the main mathematical operations in fuzzy logic. They generalize the classical two-valued implication, which takes values in \(\{0,1\}\), to fuzzy logic, where the truth values belong to the unit interval [0, 1]. This family of functions plays a significant role in the development of fuzzy systems. The study of this class of operations has been extensively developed in the last 40 years from both theoretical and applicational points of view. In our presentation we will concentrate on both streams. Firstly, we present the mathematical aspects of fuzzy implications, namely, analytical and algebraic.

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References

  1. Baczyński, M., Beliakov, G., Bustince, H., Pradera, A. (eds.): Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol. 300. Springer, Berlin (2013)

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007, Katowice, Poland

    Michał Baczyński

Authors
  1. Michał Baczyński
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Correspondence to Michał Baczyński .

Editor information

Editors and Affiliations

  1. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    Tai-He Fan

  2. Fujian, Jimei University Fujian, Xiamen, China

    Shui-Li Chen

  3. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    San-Min Wang

  4. Yanta, Shaanxi Normal University Yanta, Xi’an, China

    Yong-Ming Li

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Baczyński, M. (2017). Theoretical and Applicational Aspects of Fuzzy Implication Functions. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-46206-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46205-9

  • Online ISBN: 978-3-319-46206-6

  • eBook Packages: EngineeringEngineering (R0)

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